The kernel of \(f_{L/2L}\)  is the subspace of all \(x\)  such that \(f_{L/2L}(x,y)=0\)  for all \(y\in L/2L\)  and the
kernel of \(q_{L/2L}\)  is the subspace of all \(x\)  in the kernel of \(f_{L/2L}\)  for which also \(q_{L/2L}(x)=0\) .
We define the nullity and the rank of \(q_{L/2L}\)  to be the dimension and the codimension of
its kernel, and call \(q_{L/2L}\)  non-singular when its nullity is zero.
A subspace is called isotropic if \(q_{L/2L}(x)\)  vanishes for all \(x\)  in the subspace (see [1]}).
